Emergent Causologic: The Synergifollow Operator
A ⦶ B ≡ (A → B) ∧ (A ⊕ B) ∧ Emergent(A,B)
where Emergent(A,B) ≡ I(A;B|System) > I(A;B|Isolated)
| A | B | Emergent(A,B) | A⦶B |
|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 |
| 1 | 1 | 1 | 0 |
Emergence Theorem: Emergent(A,B) ⇒ ¬Reducible(A,B) ∧ ¬Predictable(A,B)
If B is emergent relative to A, then:
1. B is not reducible to properties of A (¬Reducible)
2. B is not predictable from isolated study of A (¬Predictable)
3. B arises only through systemic organization
Methodology for Computing Emergent(A,B)
- Define system boundaries - what constitutes System vs Isolated
- Measure mutual information under two conditions:
- Components isolated: I(A;B|Isolated)
- Components in system: I(A;B|System)
- Compute the difference: ΔI = I(System) - I(Isolated)
- Threshold value: Emergent if ΔI > ε (recommended ε = 0.1)
Concrete Examples of Emergent(A,B) Computation
Example 1: Neural Network
A = individual neuron
B = pattern recognition
I(A;B|Isolated) = 0.01 bits // neuron almost non-informative
I(A;B|System) = 0.45 bits // neuron in network significantly more informative
Emergent(A,B) = 0.45 > 0.01 = True
Example 2: River Whirlpool
A = water molecule
B = rotational motion
I(A;B|Isolated) ≈ 0 // single molecule creates no rotation
I(A;B|System) = 0.8 bits // in flow, molecule participates in motion
Emergent(A,B) = True
Example 3: Ant Colony
A = behavior of single ant
B = colony coordination
I(A;B|Isolated) = 0.02 // single ant does not coordinate colony
I(A;B|System) = 0.75 // in colony, behavior becomes informative
Emergent(A,B) = True
A ⦶ B = (A→B) ∧ (A⊕B) ∧ True = True
Example 4: Negative Case
A = ignition key
B = engine operation
I(A;B|Isolated) = 0.9 // direct causal relationship
I(A;B|System) = 0.9 // does not increase in system context
Emergent(A,B) = False
A ⦶ B = False // not emergent consequence
Semantics: "B follows from A, but A and B are distinct, and their connection is emergent"
Applications: complex systems theory, artificial intelligence, neuroscience,
philosophy of mind, verification of emergent properties.
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© 2025 [pseud.] Maximilian Logikov. License: CC-BY-SA (Creative Commons Attribution-ShareAlike).
Materials are provided for informational purposes and are not a scientific publication.
The author is not responsible for interpretation and use of the presented information.
The novelty of the concept has not been verified — the author developed it independently.
If similar ideas have already been published, priority belongs to their authors.
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